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SUMMARY:Blair Davey (Montana State University)
DTSTART:20210222T170000Z
DTEND:20210222T175000Z
DTSTAMP:20260423T024832Z
UID:anpdews/51
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/anpdews/51/"
 >A quantification of the Besicovitch projection theorem and its generaliza
 tions</a>\nby Blair Davey (Montana State University) as part of HA-GMT-PDE
  Seminar\n\n\nAbstract\nThe Besicovitch projection theorem asserts that if
  a subset E of the plane has finite length in the sense of Hausdorff and i
 s purely unrectifiable (so its intersection with any Lipschitz graph has z
 ero length)\, then almost every linear projection of E to a line will have
  zero measure. As a consequence\, the probability that a randomly dropped 
 line intersects such a set E is equal to zero.  This shows us that the Bes
 icovitch projection theorem is connected to the classical Buffon needle pr
 oblem.  Motivated by the so-called Buffon circle problem\, we explore what
  happens when lines are replaced by more general curves.  This leads us to
  discuss generalized Besicovitch theorems and the ways in which we can qua
 ntify such results by building upon the work of Tao\, Volberg\, and others
 .  This talk covers joint work with Laura Cladek and Krystal Taylor.\n
LOCATION:https://researchseminars.org/talk/anpdews/51/
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